Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma fbe7194e5ef4…

magma fbe7194e5ef4
Size
705
Isomorphism class hash
fbe7194e5ef4bd21124a069d6eb2349c1bd866790d4a7fdd74d90c7a8da84dc5
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 20:03:17
Display reorder
660,345,612,37,607,210,38,346,608,211,613,614,347,36,606,212,40,615,344,610,213,616,41,342,611,214,39,617,343,609,215,43,351,618,605,208,44,352,619,603,209,42,353,620,604,207,350,46,621,601,204,348,47,622,602,205,349,45,623,600,206,687,688,686,685,454,440,142,433,467,143,455,434,465,438,439,453,141,432,466,138,443,450,436,463,441,139,451,437,464,140,442,452,435,462,133,460,446,431,473,134,461,444,429,471,132,459,445,430,472,456,136,449,427,469,457,137,447,428,470,458,135,448,426,468,703,704,701,702,598,577,330,571,108,331,599,572,109,578,576,597,332,570,110,333,580,594,574,111,581,334,595,575,112,335,579,596,573,113,336,589,583,569,114,337,590,584,567,115,338,588,582,568,116,592,339,586,565,117,593,340,587,566,118,591,341,585,564,119,671,672,670,669,498,496,150,474,520,151,499,475,521,497,495,500,152,476,519,153,492,501,477,516,493,154,502,478,517,155,494,503,479,518,148,504,487,480,511,149,505,488,481,512,147,506,486,482,510,507,144,490,483,514,508,145,491,484,515,509,146,489,485,513,679,680,678,677,120,159,531,290,283,532,121,288,284,160,161,122,533,289,282,530,158,123,293,286,156,528,124,291,287,529,157,125,292,285,522,126,165,296,281,523,127,166,294,279,524,128,167,295,280,129,525,164,299,277,130,526,162,297,278,131,527,163,298,276,692,691,690,689,196,186,92,316,554,90,197,317,552,187,188,195,91,315,553,95,189,192,312,557,190,93,193,313,555,94,191,194,314,556,87,202,184,322,549,88,203,185,323,550,89,201,183,321,551,198,86,180,318,548,199,84,181,319,546,200,85,182,320,547,699,700,698,697,242,238,264,217,255,265,240,218,256,239,237,241,266,216,257,267,234,245,220,254,235,268,243,221,252,269,236,244,219,253,270,248,229,223,261,271,246,230,224,262,272,247,228,222,263,251,273,232,226,260,249,274,233,227,258,250,275,231,225,259,663,664,662,661,28,50,626,371,360,624,29,369,361,48,49,27,625,370,362,629,53,24,367,363,51,627,25,368,364,628,52,26,366,365,632,34,56,377,358,630,35,54,375,359,631,33,55,376,357,30,635,59,373,354,31,633,57,374,355,32,634,58,372,356,682,683,684,681,651,650,69,649,648,70,655,653,652,654,658,659,71,656,657,68,644,647,646,645,637,66,638,636,639,67,641,643,642,640,60,563,97,329,104,61,561,98,327,102,62,562,96,328,103,559,63,100,325,107,560,64,101,326,105,558,65,99,324,106,695,696,693,694,171,306,538,18,75,539,172,19,76,307,308,173,537,20,77,534,309,170,21,74,310,535,168,22,72,536,311,169,23,73,544,177,304,16,81,545,178,305,17,82,543,179,303,15,83,176,540,300,12,80,174,541,301,13,78,175,542,302,14,79,667,668,665,666,412,391,3,388,416,4,413,389,414,392,390,411,5,387,415,2,394,408,384,419,395,1,409,385,417,0,393,410,386,418,9,403,397,379,422,10,404,398,380,420,11,402,396,378,421,406,8,400,382,425,407,6,401,383,423,405,7,399,381,424,675,676,673,674 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#b88a5e69f4f2e8155017edd6b5c4ba2f90c1abf217fa4fb1e3b057bac30e1168, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 20:03:18 · history